The issue I see with the original $400 job creeping to $1000 is the client has changed things several times, requiring possibly rescheduling other clients on that day. Which does not sound like it is the case here. But I would also dare to venture that the client would also show up with more people, and other demands on the day of the shoot requiring yet another change in the contract. Then you have to deal with them not liking the photos, even if they are stunning to try to reduce the overall cost of the shoot.
In any case, they pre-pay for the entire shoot before I would even get my gear out of the car.
Exactly my thoughts. And I am requiring payment up front, for sure, if they agree to the $1,000. I just get extremely cautious when I have a client doing this. I call it project creep, and something like this rarely happens. But it happens from time to time and in the past, this is usually portentous that there are more changes that are going to happen. It's just ironic because the timing of this original post is similar to what I am dealing with this week.